Abstract

We construct the screening currents of the quantum superalgebra for an arbitrary level k ≠ −N + 1. We show that these screening currents commute with the superalgebra modulo total difference. We propose bosonizations of the vertex operators by using the screening currents. We check that these vertex operators are the intertwiners among the Fock-Wakimoto representation and the typical representation for rank N ⩽ 4.

Received 31 January 2012Accepted 18 July 2012Published online 09 August 2012

Acknowledgments:

This work is supported by the Grant-in-Aid for Scientific Research C (21540228) from Japan Society for Promotion of Science. The author would like to thank Professor Etsuro Date, Professor Hiroyuki Yamane, Professor Masato Okado, Professor Gen Kuroki, Professor Koji Hasegawa, Professor Kenji Iohara, and Professor Hitoshi Konno for their interests to this work.